124
MOVEMENT OF SMALL
PARTICLES
But
if instead of the dissolved
substance,
the partial
volume
V*
of
the
liquid
contains small
suspended
bodies that likewise
cannot
pass
through
the
solvent-permeable
wall,
then
according to
the classical
theory
of
thermo-
dynamics
we
should
not
expect-at
least if
we
neglect
the force of
gravity,
which
does not
interest
us
here-that
a
force
be exerted
on
the wall; because
according
to
the
customary
conception,
the
"free
energy"
of the
system
does
not
seem
to depend
on
the position
of
the wall
and of
the
suspended
bodies,
but
only
on
the total
masses
and properties of
the
suspended
substance, the
liquid,
and
the wall,
as
well
as on
the
pressure
and temperature.
To
be
sure,
the
energy
and entropy
of the interfaces (capillary forces) should also
be
considered in the calculation of the free
energy;
but
we can
disregard
them
since the
changes
in the
position
of the wall
and
the
suspended
bodies
considered
here shall
proceed
without
changes
in the size
and condition
of
the
contact
surfaces.
[4]
But
from
the
standpoint of
the molecular-kinetic
theory of
heat
we are
led
to
a
different
conception.
According
to
this
theory,
a
dissolved
molecule
differs
from
a
suspended
body
in
size
alone, and
it is difficult
to
see
why
suspended
bodies should
not
produce
the
same
osmotic
pressure
as
an
equal
number
of
dissolved molecules.
We
will
have
to
assume
that the
suspended
bodies
perform
an
irregular,
even though
very
slow, motion
in the liquid
due
to
the liquid's molecular
motion;
if
prevented
by
the
wall
from
leaving
the
volume
V*,
they
will
exert
forces
upon
the wall
exactly
as
dissolved
molecules
do.
Thus,
if
n
suspended
bodies
are
present
in the
volume
V*,
i.e.,
n/V
=
v
in the unit
volume, and
if the
separation between
neighboring
bodies is sufficiently
large,
there will
correspond to
them
an
osmotic
pressure
p
of
magnitude
n
_
XT
n
_
XT
P
-
y*TI-
w'u'"
where
N
denotes
the
number
of
true
molecules
per gram-molecule.
It shall
be
shown
in the
next
section
that the
molecular-kinetic
theory of
heat
does
indeed lead
to
this broader
conception
of
osmotic
pressure.